Decision trees, monotone functions, and semimatroids

We define decision trees for monotone functions on a simplicial complex. We define homology decidability of monotone functions, and show that various monotone functions related to semimatroids are homology decidable. Homology decidability is a generalization of semi-nonevasiveness, a notion due to Jonsson. The motivating example is the complex of bipartite graphs, whose Betti numbers are unknown in general. We show that these monotone functions have optimum decision trees, from which we can compute relative Betti numbers of related pairs of simplicial complexes. Moreover, these relative Betti numbers are coefficients of evaluations of the Tutte polynomial, and every semimatroid collapses onto its broken circuit complex.Comment: 16 page

Magnetically centered liquid column float Patent

Magnetically centered liquid column floa

Some Intuition behind Large Cardinal Axioms, Their Characterization, and Related Results

We aim to explain the intuition behind several large cardinal axioms, give characterization theorems for these axioms, and then discuss a few of their properties. As a capstone, we hope to introduce a new large cardinal notion and give a similar characterization theorem of this new notion. Our new notion of near strong compactness was inspired by the similar notion of near supercompactness, due to Jason Schanker

Topological Change in Mean Convex Mean Curvature Flow

Consider the mean curvature flow of an (n+1)-dimensional, compact, mean convex region in Euclidean space (or, if n<7, in a Riemannian manifold). We prove that elements of the m-th homotopy group of the complementary region can die only if there is a shrinking S^k x R^(n-k) singularity for some k less than or equal to m. We also prove that for each m from 1 to n, there is a nonempty open set of compact, mean convex regions K in R^(n+1) with smooth boundary for which the resulting mean curvature flow has a shrinking S^m x R^(n-m) singularity.Comment: 19 pages. This version includes a new section proving that certain kinds of mean curvature flow singularities persist under arbitrary small perturbations of the initial surface. Newest update (Oct 2013) fixes some bibliographic reference

Resolving the virial discrepancy in clusters of galaxies with modified Newtonian dynamics

A sample of 197 X-ray emitting clusters of galaxies is considered in the context of Milgrom's modified Newtonian dynamics (MOND). It is shown that the gas mass, extrapolated via an assumed $\beta$ model to a fixed radius of 3 Mpc, is correlated with the gas temperature as predicted by MOND ($M_g \propto T^2$). The observed temperatures are generally consistent with the inferred mass of hot gas; no substantial quantity of additional unseen matter is required in the context of MOND. However, modified dynamics cannot resolve the strong lensing discrepancy in those clusters where this phenomenon occurs. The prediction is that additional baryonic matter may be detected in the central regions of rich clusters.Comment: Submitted to A&A, 4 pages, 3 figures, A&A macro

Big boys don't cry: Depression and men

Men are a numerical minority group receiving a diagnosis of, and treatment for, depression. However, community surveys of men and of their mental health issues (e.g. suicide and alcoholism) have led some to suggest that many more men have depression than are currently seen in healthcare services. This article explores current approaches to men and depression, which draw on theories of sex differences, gender roles and hegemonic masculinity. The sex differences approach has the potential to provide diagnostic tools for (male) depression; gender role theory could be used to redesign health services so that they target individuals who have a masculine, problem-focused coping style; and hegemonic masculinity highlights how gender is enacted through depression and that men’s depression may be visible in abusive, aggressive and violent practices. Depression in men is receiving growing recognition, and recent policy changes in the UK may mean that health services are obliged to incorporate services that meet the needs of men with depression